31,145 research outputs found

### Blood oxygen saturation determined by transmission spectrophotometry of hemolyzed blood samples

Use of the Lambert-Beer Transmission Law determines blood oxygen saturation of hemolyzed blood samples. This simplified method is based on the difference in optical absorption properties of hemoglobin and oxyhemoglobin

### Improved sample capsule for determination of oxygen in hemolyzed blood

Sample capsule for determination of oxygen in hemolyzed blood consists of a measured section of polytetrafluoroethylene tubing equipped at each end with a connector and a stopcock valve. This method eliminates errors from air entrainment or from the use of mercury or syringe lubricant

### Gauge Transformations, BRST Cohomology and Wigner's Little Group

We discuss the (dual-)gauge transformations and BRST cohomology for the two
(1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional
(4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries
(and their corresponding generators) for the Lagrangian densities of these
theories. For the 4D free 2-form gauge theory, we show that the changes on the
antisymmetric polarization tensor e^{\mu\nu} (k) due to (i) the (dual-)gauge
transformations corresponding to the internal symmetry group, and (ii) the
translation subgroup T(2) of the Wigner's little group, are connected with
each-other for the specific relationships among the parameters of these
transformation groups. In the language of BRST cohomology defined w.r.t. the
conserved and nilpotent (co-)BRST charges, the (dual-)gauge transformed states
turn out to be the sum of the original state and the (co-)BRST exact states. We
comment on (i) the quasi-topological nature of the 4D free 2-form gauge theory
from the degrees of freedom count on e^{\mu\nu} (k), and (ii) the Wigner's
little group and the BRST cohomology for the 2D one-form gauge theory {\it
vis-{\`a}-vis} our analysis for the 4D 2-form gauge theory.Comment: LaTeX file, 29 pages, misprints in (3.7), (3.8), (3.9), (3.13) and
(4.14)corrected and communicated to IJMPA as ``Erratum'

### Superfield approach to a novel symmetry for non-Abelian gauge theory

In the framework of superfield formalism, we demonstrate the existence of a
new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the
BRST invariant Lagrangian density of a self-interacting two ($1 +
1$)-dimensional (2D) non-Abelian gauge theory (having no interaction with
matter fields). The local and nilpotent Noether conserved charges corresponding
to the above continuous symmetries find their geometrical interpretation as the
translation generators along the odd (Grassmannian) directions of the four ($2
+ 2)$-dimensional supermanifold.Comment: LaTeX, 12 pages, equations (4.2)--(4.6) correcte

### Equivalent Binary Quadratic Form and the Extended Modular Group

Extended modular group $\bar{\Pi}=$, where
R:z\rightarrow -\bar{z}, \sim
T:z\rightarrow\frac{-1}{z},\simU:z\rightarrow\frac{-1}{z +1} , has been used
to study some properties of the binary quadratic forms whose base points lie in
the point set fundamental region $F_{\bar{\Pi}}$ (See \cite{Tekcan1, Flath}).
In this paper we look at how base points have been used in the study of
equivalent binary quadratic forms, and we prove that two positive definite
forms are equivalent if and only if the base point of one form is mapped onto
the base point of the other form under the action of the extended modular group
and any positive definite integral form can be transformed into the reduced
form of the same discriminant under the action of the extended modular group
and extend these results for the subset \QQ^*(\sqrt{-n}) of the imaginary
quadratic field \QQ(\sqrt{-m}).Comment: Paper contains two figures and twelve page

### Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and
anti-BRST symmetry transformations for {\it all} the fields of a free Abelian
2-form gauge theory by exploiting the geometrical superfield approach to BRST
formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a
(4, 2)-dimensional supermanifold parameterized by the four even spacetime
variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian
variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta
\bar\theta + \bar\theta \theta = 0). One of the salient features of our present
investigation is that the above nilpotent (anti-)BRST symmetry transformations
turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari
(CF) type of restriction. The latter condition emerges due to the application
of our present superfield formalism. The actual CF condition, as is well-known,
is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that
our present 4D Abelian 2-form gauge theory imbibes some of the key signatures
of the 4D non-Abelian 1-form gauge theory. We briefly comment on the
generalization of our supperfield approach to the case of Abelian 3-form gauge
theory in four (3 + 1)-dimensions of spacetime.Comment: LaTeX file, 23 pages, journal versio

### An Alternative To The Horizontality Condition In Superfield Approach To BRST Symmetries

We provide an alternative to the gauge covariant horizontality condition
which is responsible for the derivation of the nilpotent (anti-)BRST symmetry
transformations for the gauge and (anti-)ghost fields of a (3 + 1)-dimensional
(4D) interacting 1-form non-Abelian gauge theory in the framework of the usual
superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. The above
covariant horizontality condition is replaced by a gauge invariant restriction
on the (4, 2)-dimensional supermanifold, parameterized by a set of four
spacetime coordinates x^\mu (\mu = 0, 1, 2, 3) and a pair of Grassmannian
variables \theta and \bar\theta. The latter condition enables us to derive the
nilpotent (anti-)BRST symmetry transformations for all the fields of an
interacting 4D 1-form non-Abelian gauge theory where there is an explicit
coupling between the gauge field and the Dirac fields. The key differences and
striking similarities between the above two conditions are pointed out clearly.Comment: LaTeX file, 20 pages, journal versio

### Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism

In the framework of augmented superfield approach, we provide the geometrical
origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST
charges and a non-nilpotent bosonic charge. Together, these local and conserved
charges turn out to be responsible for a clear and cogent definition of the
Hodge decomposition theorem in the quantum Hilbert space of states. The above
charges owe their origin to the de Rham cohomological operators of differential
geometry which are found to be at the heart of some of the key concepts
associated with the interacting gauge theories. For our present review, we
choose the two $(1 + 1)$-dimensional (2D) quantum electrodynamics (QED) as a
prototype field theoretical model to derive all the nilpotent symmetries for
all the fields present in this interacting gauge theory in the framework of
augmented superfield formulation and show that this theory is a {\it unique}
example of an interacting gauge theory which provides a tractable field
theoretical model for the Hodge theory.Comment: LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the
Journal are give

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